Continuous Frequency Distribution

This kind of classification is most popular in practice. The following technical terms are very important when a continuous frequency distribution is formed and the data is classified according to class intervals.

Class limit: The class limit is the lowest & the highest values that can be included in the class. For e.g. take the class 20- 40 the lowest value of the class is 20 and the highest is 40. The two boundaries for calls are termed as the lower limit and the upper limit. The lower limit of a class is the value below which there are no items in the class. The upper limit of a class is the value above which no item can belong to that class. Of the class 70-89, 70 is the lower limit and 89 is the upper limit. In this class there is no value which is less than 70 or more than 89. Similarly if we take the class 90- 109 then there is no value in that class which is less than 90 ore more than 109. The way in which the class limits are stated basically depends upon the nature of the data.

Class intervals: The difference between the upper and lower limit of a class is termed as class interval of that calls. For e.g. in the class 100-200 the class interval (200-100) is 100. An important decision while construction a frequency distribution is about the width of the class interval whether it should be 10, 20, 50, 100, 500 etc. the decision would depend upon the number of factor like the range in the data, the difference between the smallest and largest item, the details required and the number of classes to be formed etc. The simple formula to obtain the estimation of the appropriate class interval I is

 I = [(L-S)/k]

 Where, L = largest item

 S = smallest item

 K = the number of classes

For e.g. if the salary of 100 employees in a commercial undertaking ranges between $ 500 and $ 5,5000 and we want to form 10 classes, then the class interval would be

I = [(L - S)/k]

L = 5,500, S = 5000, k + 10

I = I = 5500 - (500/10) = 5000/10 = 500

The starting calls would be 500 - 1,000, the next 1,000 - 1,500, and so on.

The question now is how to fix the number of classes?

k is the number that can either be fixed arbitrarily, keeping in view that the nature of problem under study or it can be decided with the help of surges rule. According to him the number of classes can be determined by the formula:

K = 1 + 3.322 log N

Where N = total number of observation

And log = logarithms of the number

Thus if 10 observations are being studied the number of classes be

K = 1 + (3.322 x]) = 4.322 or 4.

And if 100 observations are being studied the number of classes be

K = 1 + (3.322x2) = 1 + 6.644 = 7.644 or 8.

It must be noted that as log is used in the formula the number of classes will normally be between 4 and 20- It cannot be less than 4 even if N is less than 10 and if n is 1 million k will be 1 + (3.323 x 6) = 20.9 or 21.

Surgis suggested the following formula for determining the magnitude of class interval:

I = range/1 + 3.322 log N

Where range is the difference between the largest & smallest items,

For e.g. if in the above illustration we apply this formula the magnitude of class interval be

I = 550 - (500/1) + (3.322 x 2) = 5000/7.644 = 654.1 or 650

If we take a class interval of 650, then the number of classes formed would be 500/ 65, 7.69 or 8.

It may be remembered that the application of above formula may give a value involving fractions and odd intervals. For e.g. we got I = 6.541. In such cases the suitable approximation should be made.

Class frequency

The number of observations corresponding to a particular class is termed as the frequency of that class or the class frequency. In the following example the frequency of the class 1000-1100 is 50 which imply that there are 50 persons having income between $ 1000 and $ 1100. If we add together the all the frequencies of all individual classes, we obtain the total frequency. Thus in the same problem the total frequency of  six classes is 50 that means that in all there are 550 persons whose income has been studied.

Class mid-point or class mark

It is the value lying half-way between the lower and upper class limits of a class-interval. The mid-point of a class is ascertained as follows:

Mid-point of a class = [(upper limit of the class + lower limit of the class)/2]

For the aim of further calculation in statistical we take the mid-point of each class to represent that class.

There are two methods of classifying the data according to class-intervals viz. (i) exclusive method and (ii) inclusive method.